The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  1  2  1  2  2  2  1  2  2  2  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  0  0  2  0  2  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  0  2  2  0  0  0  2  0  0  2  2
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  2  2  2  2  0  2  2  0  2  0  2  2  0  2
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  2  0  2  0  2  2  0  2  0  2  2  2  0  2  0  2  2
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  2  0  2  0  2  2  2  2  0  2  2  2  0  2  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  0  2  2  2  0  0  2  2  2  2  2  2  0
 0  0  0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  2  0  0  2  2  2  2  0  0  2  2  2  0  0
 0  0  0  0  0  0  0  0  0  2  0  0  2  0  0  0  2  0  0  2  2  0  0  2  0  2  2  0  2  2  0
 0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2  0  0  2  2  2  0  0  2  0  2  0  2  2
 0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  0  2  0  2  0  2  2  2  2  2  0  0  0

generates a code of length 31 over Z4 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+232x^20+8x^22+631x^24+288x^26+1568x^28+1008x^30+2214x^32+672x^34+1098x^36+72x^38+313x^40+76x^44+9x^48+2x^52

The gray image is a code over GF(2) with n=62, k=13 and d=20.
This code was found by Heurico 1.16 in 72.7 seconds.